Question

Susan is buying black and green olives from the Olive bar for her party. She buys 4 pounds of olives. Black olives cost three dollars a pound. Green olives cost five dollars a pound. She spends $15.50. How many pounds of each type of olives does she buy? Write and solve a system of equations. Give the answer to in context of the problem.

Answer 1

Answer:

She buy 0.5 pounds of black olives and 3.5 pounds of green olives.

Step-by-step explanation:

Given:

Susan is buying black and green olives from the Olive bar for her party. She buys 4 pounds of olives.

Black olives cost three dollars a pound. Green olives cost five dollars a pound.

She spends $15.50.

Now, to find the pounds of olives she buy.

Let the pounds of black olives be $x.$

And the pounds of green olives be $y.$

So, total pounds of olives:

$x+y=4$

$x=4-y$    ........( 1 )

As, given the cost of black olives $3 a pound.

And cost of green olives $4 a pound.

Now, the total money spends:

$3x+4y=15.50$

Substituting the value of $x$ from equation (1) we get:

$3(4-y)+4y=15.50$

$12-3y+4y=15.50$

$12+y=15.50$

Subtracting both sides by 12 we get:

$y=3.5$

The green olives = 3.5 pounds.

Now, substituting the value of $y$ in equation (1):

$x=4-y\\x=4-3.5\\x=0.5\ pounds.$

The black olives = 0.5 pounds.

Therefore, she buy 0.5 pounds of black olives and 3.5 pounds of green olives.